Learn French: Elle était tellement fatiguée. Tu l'as deviné ?

It is the neuter object pronoun le (shortened before a vowel). It doesn't replace a specific noun, but rather the entire previous idea: Elle était tellement fatiguée. In English, we usually translate this as 'that' or 'it'.

Since Elle and fatiguée are feminine, shouldn't it be Tu l'as devinée with an extra 'e'?

No, because the l' here replaces a whole sentence or idea, not a specific feminine noun. When le acts as a neuter pronoun for an idea, it does not trigger feminine or plural agreement on the past participle, so deviné stays exactly as it is.

Could I use si instead of tellement here?

Yes! Elle était si fatiguée means exactly the same thing. Tellement is very common in everyday spoken French, while si can sound just a tiny bit more formal, but both are perfectly correct for saying 'so tired'.

Why do we need the l' at all? Can't I just say Tu as deviné ?

In English, we can just ask 'Did you guess?', but French verbs like deviner usually need a direct object. You have to say that you guessed 'it' or 'that', which is why the neuter pronoun le is used here to fill that spot.